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Question
Equation of a common tangent to the curves and
y2=8x and xy=−1 is
y2=8x and xy=−1 is
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Solution
The correct option is D y = x +2
y2=8x,xy=−1LetP(t,−1t)be any point on xy=−1Equation of the tangent to xy=−1 at P(t,−1t)isxy1+yx12=−1−xt+yt=−2y=xt2+(−2t)…(1)If(1)is tangent to the parabola y2=8x them−2t=21/t2⇒t3=−1t=−1∴Common tangent is y=x+2
y2=8x,xy=−1LetP(t,−1t)be any point on xy=−1Equation of the tangent to xy=−1 at P(t,−1t)isxy1+yx12=−1−xt+yt=−2y=xt2+(−2t)…(1)If(1)is tangent to the parabola y2=8x them−2t=21/t2⇒t3=−1t=−1∴Common tangent is y=x+2
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